My question to him would be how would he know if a "rootkill" is on your pc? Does your phone have a "rootkill" as well because it seems to have the same issue. Sounds like the guy is just stringing you along and he doesn't have a clue what he's talking about from his script.
As Maud said, quick way to find out would be to run the tools he has shown. I'd also add HitManPro and use the 30 day trial to scan and clean your machine. It seems to find things that malwarebytes misses and they work well together. Needless to say, I doubt you have a rootkit none the less.
Netgear wireless has always been shoddy in the first place and i've had numerous wireless issues with those pieces of crap.
Edit:
150 for removal of a virus/malware/trojan/etc is a little steep but my clients pay 135 an hour. You could always go a try your luck with GeekSquad, you'll probably be charged for 8 hours of labor and the issue will still be there though (NOT RECOMMENDED BTW).